Consumption-based capital asset pricing models: issues and controversies

This paper discusses the issues and controversies surrounding consumption-based capital asset pricing models (CCAPMs). While CCAPMs provide a chance to explain the phenomena observed in stock markets, their viability is jeopardized owing to the weak predictability of the equity premium and risk-free rate puzzles. Even given market frictions and market incompleteness, CCAPMs must test their validity constantly in the face of the formidable challenges of rival models. Measurement error with respect to time aggregation is also regarded as a major threat, causing the low volatility of consumption and eventually resulting in chaining itself to weak return predictability. In addition, the dual choice problem of portfolio and consumption rooted in CCAPMs guides us into how investors accumulate wealth through the financial market to reach the zenith of expected utility. This paper offers insights as well as understanding into the behavior of an agent and market phenomena in the context of a consumption-based economy.     

Information and capital asset pricing

Investors in a market frequently update their diverse perceptions of the values of risky assets, thus invalidating the classic capital asset pricing model's (CAPM) assumption of complete agreement among investors. To accommodate information asymmetry and belief updating, we have developed an empirically testable information-adjusted CAPM, which states that the expected excess return of a risky asset/portfolio is solely determined by the information-adjusted beta rather than the market beta. The model is then used to analyze empirical anomalies of the classic CAPM, including a flatter relation between average return and the market beta than the CAPM predicts, a non-zero Jensen's alpha, insignificant explanatory power of the market beta, and size effect.     

A liquidity-augmented capital asset pricing model

Using a new measure of liquidity, this paper documents a significant liquidity premium robust to the CAPM and the Fama–French three-factor model and shows that liquidity is an important source of priced risk. A two-factor (market and liquidity) model well explains the cross-section of stock returns, describing the liquidity premium, subsuming documented anomalies associated with size, long-term contrarian investment, and fundamental (cashflow, earnings, and dividend) to price ratios. In particular, the two-factor model accounts for the book-to-market effect, which the Fama–French three-factor model fails to explain.     

Testing multi-beta asset pricing models

This paper presents a complete solution to the estimation and testing of multi-beta models by providing a small sample likelihood ratio test when the usual normality assumption is imposed and an almost analytical GMM test when the normality assumption is relaxed. Using 10 size portfolios from January 1926 to December 1994, we reject the joint efficiency of the CRSP value-weighted and equal-weighted indices. We also apply the tests to analyze a new version of Fama and French's [Fama, E.F., French, K.R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics. 33, 3–56.] three-factor model in addition to two standard ones, and find that the new version performs the best.     

Capital gains tax and the capital asset pricing model

This paper develops a version of the Capital Asset Pricing Model that views dividend imputation as affecting company tax and assumes differential taxation of capital gains and ordinary income. These taxation issues aside, the model otherwise rests on the standard assumptions including full segmentation of national capital markets. It also treats dividend policy as exogenously determined. Estimates of the cost of equity based on this model are then compared with estimates based on the version of the CAPM typically applied in Australia, which differs only in assuming equality of the tax rates on capital gains and ordinary income. The differences between the estimates can be material. In particular, with a high dividend yield, allowance for differential taxation can result in an increase of two to three percentage points in the estimated cost of equity. The overall result obtained here carries over to a dividend equilibrium, in which firms choose a dividend policy that is optimal relative to the assumed tax structure.     

Econometric evaluation of asset pricing models

In this article we provide econometric tools for the evaluationof intertemporal asset pricing models using specification-errorand volatility bounds. We formulate analog estimators of thesebounds, give conditions for consistency, and derive the limitingdistribution of these estimators. The analysis incorporatesmarket frictions such as short-sale constraints and proportionaltransactions costs. Among several applications we show how touse the methods to assess specific asset pricing models andto provide non-parametric characterizations of asset pricinganomalies.     

The St. Petersburg paradox and capital asset pricing

Durand (J Finance 12:348–363, 1957) shows that the classical St. Petersburg paradox can apply to the valuation of a firm whose dividends grow at a constant rate forever. To capture a more realistic pattern of dividends, we model the dividend growth rate as a mean reverting process, and then use the capital asset pricing model to derive the risk-adjusted present value. The model generates an equivalent St. Petersburg game. The long-run growth rate of the payoffs (dividends) is dominant in driving the value of the game (firm), and the condition under which the value is finite is less restrictive than that of the standard game.     

International capital asset pricing: Evidence from options

We study the risk dynamics and pricing in international economies through a joint analysis of the time-series returns and option prices on three equity indexes underlying three economies: the S&P 500 Index of the United States, the FTSE 100 Index of the United Kingdom, and the Nikkei-225 Stock Average of Japan. We develop an international capital asset pricing model, under which the return on each equity index is decomposed into two orthogonal jump-diffusion components: a global component and a country-specific component. We apply separate stochastic time changes to the two components so that stochastic volatility can come from both global and country-specific risks. For each economy, we assign separate market prices for the two return risk components and the two volatility risk components. Under this specification, we obtain tractable option pricing solutions. Model estimation reveals several interesting insights. First, global and country-specific return and volatility risks show different dynamics. Global return movements contain a larger discontinuous component, and global return volatility is more persistent than the country-specific counterparts. Second, investors charge positive prices for global return risk and negative prices for volatility risk, suggesting that investors are willing to pay positive premiums to hedge against downside global return movements and upside volatility movements. Third, the three economies contain different risk profiles and also price risks differently. Japan contains the largest idiosyncratic risk component and smallest global risk component. Investors in the Japanese market also price more heavily against future volatility increases than against future market downfalls.     

A note on capital asset pricing and heterogeneous taxes

In this paper, we present a stylized model where we show how asset prices, i.e., required expected rates of returns, may be characterized in a world with heterogeneous asset taxes. Within a simple CAPM-like framework, we derive an after-tax beta equal to the pre-tax beta multiplied by a (non-obvious) asset specific tax adjustment. We further show in what sense the Security Market Line here can be replaced by a Security Market Fan. Well-known CAPM relations are obtained as special cases, and policy implications are analyzed.     

An intertemporal capital asset pricing model with heterogeneous expectations

This paper extends the intertemporal capital asset pricing model (ICAPM) to integrate the heterogeneous trading behavior of three groups of investors; rational utility maximizers, positive feedback, or momentum, traders, and fundamental traders. Using several contemporary fundamental factors to proxy for the latter of these investors’ trading patterns, the interaction of these three groups of investors is explored in the G-7 markets using monthly stock market prices. There is no evidence that positive feedback traders are present in the sample data. Fundamental traders are however observable. This finding suggests that although positive feedback traders may drive stock prices in the short-run, as is typically observed in higher frequency data, fundamental traders likely play a role in pushing prices back to their fundamental value in the longer-run.     

The intertemporal capital asset pricing model with dynamic conditional correlations

The intertemporal capital asset pricing model of Merton (1973) is examined using the dynamic conditional correlation (DCC) model of Engle (2002). The mean-reverting DCC model is used to estimate a stock’s (portfolio’s) conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock’s (portfolio’s) expected return. The risk-aversion coefficient, restricted to be the same across assets in panel regression, is estimated to be between two and four and highly significant. The risk premium induced by the conditional covariation of assets with the market portfolio remains positive and significant after controlling for risk premia induced by conditional covariation with macroeconomic, financial, and volatility factors.     

Extending the capital asset pricing model: the reward beta approach

This paper offers an alternative method for estimating expected returns. The proposed reward beta approach performs well empirically and is based on asset pricing theory. The empirical section compares this approach with the capital asset pricing model (CAPM) and the Fama–French three‐factor model. In out‐of‐sample testing, both the CAPM and the three‐factor model are rejected. In contrast, the reward beta approach easily passes the same test. In robustness checks, the reward beta approach consistently outperforms both the CAPM and the three‐factor model.     

Specification tests of asset pricing models using excess returns

In this paper, we discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. We point out that the popular way of specifying the stochastic discount factor (SDF) as a linear function of the factors is problematic because (1) the specification test statistic is not invariant to an affine transformation of the factors, and (2) the SDFs of competing models can have very different means. In contrast, an alternative specification that defines the SDF as a linear function of the de-meaned factors is free from these two problems and is more appropriate for model comparison. In addition, we suggest that a modification of the traditional Hansen–Jagannathan distance (HJ-distance) is needed when we use the de-meaned factors. The modified HJ-distance uses the inverse of the covariance matrix (instead of the second moment matrix) of excess returns as the weighting matrix to aggregate pricing errors. Asymptotic distributions of the modified HJ-distance and of the traditional HJ-distance based on the de-meaned SDF under correctly specified and misspecified models are provided. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification. We show that failure to take model misspecification into account is likely to understate the standard errors of the estimates of the SDF parameters and lead us to erroneously conclude that certain factors are priced.     

Inference in asset pricing models with a low-variance factor

This paper concerns with the effects of including a low-variance factor in an asset pricing model. When a low-variance factor is present, the commonly applied Fama–MacBeth two-pass regression procedure is very likely to yield misleading results. Local asymptotic analysis and simulation evidence indicate that the risk premiums corresponding to all factors are very likely to be unreliably estimated. Moreover, t- and F-statistics are less likely to detect whether the risk premiums are significantly different from zero. We recommend Kleibergen’s (2009)FAR statistic when there is a low-variance factor included in an asset pricing model.     

Beta lives - some statistical perspectives on the capital asset pricing model

This note summarizes some technical issues relevant to the use of the idea of excess return in empirical modelling. We cover the case where the aim is to construct a measure of expected return on an asset and a model of the CAPM type is used. We review some of the problems and show examples where the basic CAPM may be used to develop other results which relate the expected returns on assets both to the expected return on the market and other factors.     

The restrictions on predictability implied by rational asset pricing models

This article shows how rational asset pricing models restrictthe regression-based criteria commonly used to measure returnpredictability. Specifically it invokes no-arbitrage argumentsto show that the intercept, slope coefficients, and R² in predictiveregressions must take specific values. These restrictions providea way to directly assess whether the predictability uncoveredusing regression analysis is consistent with rational pricing.Empirical tests reveal that the returns on the CRSP size decilesare too predictable to be compatible with a number of well-knownpricing models. However, the overall pattern of predictabilityacross these portfolios is reasonably consistent with what wewould expect under circumstances where predictability is rational.     

Measuring portfolio performance and the empirical content of asset pricing models

Recent work by Richard Roll has challenged the worth of portfolio performance measures based on the capital asset pricing model. This paper demonstrates that Roll's conclusions are due to his focusing on a ‘truly’ ex-ante efficient index. Using a choice and information theoretic framework, we show that an appropriate index is efficient relative to the probabilities assessed by the ‘market’. Residual analyses and portfolio performance tests, using such an index, yield meaningful results for a wide class of information structures. Roll's primary criticisms, however, relate to tests of the asset pricing model itself. We argue that these criticisms are vastly overstated.     

Corporate sustainability in asset pricing models and mutual funds performance measurement

This study explores whether corporate sustainability is a relevant factor in multifactor asset pricing models. It contributes to the literature on asset pricing, as well as to the literature that examines how sustainability impacts capital markets, by constructing a new factor that captures differences in the returns of sustainable and non-sustainable firms. Specifically, it examines whether an additional sustainability factor has explanatory power in asset pricing models that include size, book-to-market equity, and momentum factors. This research has practical implications for the performance measurement of portfolios and mutual funds that are managed in accordance with sustainability criteria in that it disentangles general stock-picking skills from the differences in returns between sustainable and non-sustainable stocks.     

Testing conditional asset pricing models: An emerging market perspective

The CAPM as the benchmark asset pricing model generally performs poorly in both developed and emerging markets. We investigate whether allowing the model parameters to vary improves the performance of the CAPM and the Fama–French model. Conditional asset pricing models scaled by conditioning variables such as Trading Volume and Dividend Yield generally result in small pricing errors. However, a graphical analysis reveals that the predictions of conditional models are generally upward biased. We demonstrate that the bias in prediction may be the consequence of ignoring frequent large variation in asset returns caused by volatile institutional, political and macroeconomic conditions. This is characterised by excess kurtosis. An unconditional Fama–French model augmented with a cubic market factor performs the best among some competing models when local risk factors are employed. Moreover, the conditional models with global risk factors scaled by global conditioning variables perform better than the unconditional models with global risk factors.